Problem: Natasha is going to fly on a rocket to Mars and return to Earth. Also, on the way to Mars, she will land on n - 2 intermediate planets. Formally: we number all the planets from 1 to n. 1 is Earth, n is Mars. Natasha will make exactly n flights: 1 → 2 → … n → 1.

Flight from x to y consists of two phases: take-off from planet x and landing to planet y. This way, the overall itinerary of the trip will be: the 1-st planet → take-off from the 1-st planet → landing to the 2-nd planet → 2-nd planet → take-off from the 2-nd planet → … → landing to the n-th planet → the n-th planet → take-off from the n-th planet → landing to the 1-st planet → the 1-st planet.

The mass of the rocket together with all the useful cargo (but without fuel) is m tons. However, Natasha does not know how much fuel to load into the rocket. Unfortunately, fuel can only be loaded on Earth, so if the rocket runs out of fuel on some other planet, Natasha will not be able to return home. Fuel is needed to take-off from each planet and to land to each planet. It is known that 1 ton of fuel can lift off a_i tons of rocket from the i-th planet or to land b_i tons of rocket onto the i-th planet. 

For example, if the weight of rocket is 9 tons, weight of fuel is 3 tons and take-off coefficient is 8 (a_i = 8), then 1.5 tons of fuel will be burnt (since 1.5 ⋅ 8 = 9 + 3). The new weight of fuel after take-off will be 1.5 tons. 

Please note, that it is allowed to burn non-integral amount of fuel during take-off or landing, and the amount of initial fuel can be non-integral as well.

Help Natasha to calculate the minimum mass of fuel to load into the rocket. Note, that the rocket must spend fuel to carry both useful cargo and the fuel itself. However, it doesn't need to carry the fuel which has already been burnt. Assume, that the rocket takes off and lands instantly.

Input

The first line contains a single integer n (2 ≤ n ≤ 1000) — number of planets.

The second line contains the only integer m (1 ≤ m ≤ 1000) — weight of the payload.

The third line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 1000), where a_i is the number of tons, which can be lifted off by one ton of fuel.

The fourth line contains n integers b_1, b_2, …, b_n (1 ≤ b_i ≤ 1000), where b_i is the number of tons, which can be landed by one ton of fuel. 

It is guaranteed, that if Natasha can make a flight, then it takes no more than 10^9 tons of fuel.

Output

If Natasha can fly to Mars through (n - 2) planets and return to Earth, print the minimum mass of fuel (in tons) that Natasha should take. Otherwise, print a single number -1.

It is guaranteed, that if Natasha can make a flight, then it takes no more than 10^9 tons of fuel.

The answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}. Formally, let your answer be p, and the jury's answer be q. Your answer is considered correct if \frac{|p - q|}{max{(1, |q|)}} ≤ 10^{-6}.

Examples

Input

2
12
11 8
7 5


Output

10.0000000000


Input

3
1
1 4 1
2 5 3


Output

-1


Input

6
2
4 6 3 3 5 6
2 6 3 6 5 3


Output

85.4800000000

Note

Let's consider the first example.

Initially, the mass of a rocket with fuel is 22 tons.

  * At take-off from Earth one ton of fuel can lift off 11 tons of cargo, so to lift off 22 tons you need to burn 2 tons of fuel. Remaining weight of the rocket with fuel is 20 tons.
  * During landing on Mars, one ton of fuel can land 5 tons of cargo, so for landing 20 tons you will need to burn 4 tons of fuel. There will be 16 tons of the rocket with fuel remaining.
  * While taking off from Mars, one ton of fuel can raise 8 tons of cargo, so to lift off 16 tons you will need to burn 2 tons of fuel. There will be 14 tons of rocket with fuel after that.
  * During landing on Earth, one ton of fuel can land 7 tons of cargo, so for landing 14 tons you will need to burn 2 tons of fuel. Remaining weight is 12 tons, that is, a rocket without any fuel.



In the second case, the rocket will not be able even to take off from Earth.

Solution (in JAVA):

Solution:
import java.util.*;
import java.awt.List;
import java.io.*;
import java.lang.*;
import java.lang.reflect.Array;

public class code3 {

	
	
	public static void main(String[] args) {
		InputReader in = new InputReader(System.in);
		PrintWriter pw = new PrintWriter(System.out);

		// Code starts..

		

		int n = in.nextInt();
		int m = in.nextInt();
		int[] take = new int[n];
		int[] land = new int[n];
		
		
		for(int i=0; i<n; i++)
			take[i] = in.nextInt();
		for(int i=0; i<n; i++)
			land[i] = in.nextInt();
		
		
		double fuel = m;
		double x = 0;
		x = (fuel)/(land[0]-1);
		fuel += x;
		//pw.println(x);
		
		for(int i=n-1; i>=1; i--)
		{
			x = (fuel)/(take[i]-1);
			fuel += x;
			//pw.println(x);
			x = (fuel)/(land[i]-1);
			fuel += x;
			//pw.println(x);
		}
		x = (fuel)/(take[0]-1);
		fuel += x;
	
		if(fuel>100000000000000000L)
			pw.println(-1);
		else
			pw.println(fuel-m);
		// code ends...

		pw.flush();
		pw.close();
	}

	public static double pow(double x, int n)
	{
		
		double ans = 1;
		for(int i=0; i<n; i++)
			ans *= x;
		return ans;
	}
	
	
	public static boolean check(String s1, String s2){
           
		
		boolean status = true;
 
        if(s1.length() != s2.length())
        {
            status = false;
        }
        else {
            char[] s1Array = s1.toLowerCase().toCharArray();
 
            char[] s2Array = s2.toLowerCase().toCharArray();
            Arrays.sort(s1Array);
            Arrays.sort(s2Array);
            status = Arrays.equals(s1Array, s2Array);
        }
        if(status)
        	return true;
        	
        	return false;
    }
	
	    
	
	
	
	public static long[][] mul(long[][] a, long[][] b){
		
		
		int n = a.length;
		int m = b[0].length;
		long[][] c = new long[n][m];
		
		for(int i=0; i<n; i++)
			for(int j=0; j<m; j++)
			{
				long tmp = 0;
				for(int k=0; k<a[0].length; k++)
					tmp =( (tmp+mod)%mod+(a[i][k]*b[k][j]+mod)%mod)%mod;
				c[i][j] = (tmp+mod)%mod;
			}
		
		return c;
	}
	
	
	
	public static long[][] pow(long[][] a,int  n)
	{
		
		long[][] res = a;
		while(n>0)
		{
			if(n%2==1)
			{
				res = mul(a, res);
			}
			
			a = mul(a, a);
			
			n/=2;
			
			
		}
		
		return res;
		
		
	}
	
	
	
	
	

	
	
	

	
	public static boolean isSubSequence(char[] str2, String str1) {

		int j = 0;
		int m = str1.length();
		int n = str2.length;

		for (int i = 0; i < n && j < m; i++)

			if (str1.charAt(j) == str2[i])

				j++;

		return (j == m);
	}

	static class InputReader {

		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}

		public String readString() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}

	public static long c = 0;

	public static long mod = (long)Math.pow(10, 6)+3;
	public static int d;
	public static int p;
	public static int q;
	public static boolean flag;
	//public static long INF = Long.MAX_VALUE;

	public static void factSieve(int[] fact, long n) {

		for (int i = 2; i <= n; i += 2)
			fact[i] = 2;

		for (int i = 3; i <= n; i += 2) {
			if (fact[i] == 0) {
				fact[i] = i;

				for (int j = i; (long) j * i <= n; j++) {
					fact[(int) ((long) i * j)] = i;
				}
			}
		}

		/*
		 * int k = 1000; while(k!=1) { System.out.print(a[k]+" "); k /= a[k];
		 * 
		 * }
		 */
	}

	public static long floorsqrt(long n) {
		long ans = 0;
		long l = 0;
		long r = n;
		long mid = 0;
		while (l <= r) {
			mid = (l + r) / 2;
			if (mid * mid == n)
				return mid;

			if (mid * mid > n) {
				r = mid - 1;
			} else {
				ans = mid;
				l = mid + 1;
			}

		}

		return ans;
	}

	public static long fun(int[] a, int[] b, int m, int n) {
		long result = 0;
		for (int i = 0; i < m; i++)
			for (int j = 0; j < m; j++) {
				long[] fib = new long[Math.max(2, n + 2)];
				fib[1] = a[i];
				fib[2] = b[j];
				for (int k = 3; k <= n; k++)
					fib[k] = (fib[k - 1] % mod + fib[k - 2] % mod) % mod;
				result = (result % mod + fib[n] % mod) % mod;
			}

		return result;

	}

	/*
	 * public static double slope(pair p1, pair p2) { double m = INF; if((p1.x -
	 * p2.x)!=0) m = p1.y - p2.y/(p1.x - p2.x);
	 * 
	 * 
	 * return Math.abs(m);
	 * 
	 * }
	 */

	public static int gcd(int p2, int p22) {
		if (p2 == 0)
			return (int) p22;
		return gcd(p22 % p2, p2);
	}

	public static int findGCD(int arr[], int n) {
		int result = arr[0];
		for (int i = 1; i < n; i++)
			result = gcd(arr[i], result);

		return result;
	}

	public static void nextGreater(long[] a, int[] ans) {

		Stack<Integer> stk = new Stack<>();
		stk.push(0);

		for (int i = 1; i < a.length; i++) {

			if (!stk.isEmpty()) {
				int s = stk.pop();
				while (a[s] < a[i]) {
					ans[s] = i;
					if (!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if (a[s] >= a[i])
					stk.push(s);
			}

			stk.push(i);

		}
		return;

	}

	public static void nextGreaterRev(long[] a, int[] ans) {

		int n = a.length;
		int[] pans = new int[n];
		Arrays.fill(pans, -1);
		long[] arev = new long[n];
		for (int i = 0; i < n; i++)
			arev[i] = a[n - 1 - i];

		Stack<Integer> stk = new Stack<>();
		stk.push(0);

		for (int i = 1; i < n; i++) {

			if (!stk.isEmpty()) {
				int s = stk.pop();
				while (arev[s] < arev[i]) {
					pans[s] = n - i - 1;
					if (!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if (arev[s] >= arev[i])
					stk.push(s);
			}

			stk.push(i);

		}

		// for(int i=0; i<n; i++)
		// System.out.print(pans[i]+" ");

		for (int i = 0; i < n; i++)
			ans[i] = pans[n - i - 1];

		return;

	}


	public static void nextSmallerRev(int[] a, int[] ans) {

		int n = a.length;
		int[] pans = new int[n];
		Arrays.fill(pans, -1);
		long[] arev = new long[n];
		for (int i = 0; i < n; i++)
			arev[i] = a[n - 1 - i];

		Stack<Integer> stk = new Stack<>();
		stk.push(0);

		for (int i = 1; i < n; i++) {

			if (!stk.isEmpty()) {
				int s = stk.pop();
				while (arev[s] > arev[i]) {
					pans[s] = n - i - 1;
					if (!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if (arev[s] <= arev[i])
					stk.push(s);
			}

			stk.push(i);

		}

		// for(int i=0; i<n; i++)
		// System.out.print(pans[i]+" ");

		for (int i = 0; i < n; i++)
			ans[i] = pans[n - i - 1];

		return;

	}

	
	public static void nextSmaller(int[] a, int[] ans) {

		Stack<Integer> stk = new Stack<>();
		stk.push(0);

		for (int i = 1; i < a.length; i++) {

			if (!stk.isEmpty()) {
				int s = stk.pop();
				while (a[s] > a[i]) {
					ans[s] = i;
					if (!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if (a[s] <= a[i])
					stk.push(s);
			}

			stk.push(i);

		}
		return;

	}

	public static long lcm(int[] numbers) {
		long lcm = 1;
		int divisor = 2;
		while (true) {
			int cnt = 0;
			boolean divisible = false;
			for (int i = 0; i < numbers.length; i++) {
				if (numbers[i] == 0) {
					return 0;
				} else if (numbers[i] < 0) {
					numbers[i] = numbers[i] * (-1);
				}
				if (numbers[i] == 1) {
					cnt++;
				}
				if (numbers[i] % divisor == 0) {
					divisible = true;
					numbers[i] = numbers[i] / divisor;
				}
			}
			if (divisible) {
				lcm = lcm * divisor;
			} else {
				divisor++;
			}
			if (cnt == numbers.length) {
				return lcm;
			}
		}
	}

	public static long fact(long n) {

		long factorial = 1;
		for (int i = 1; i <= n; i++) {
			factorial *= i;
		}
		return factorial;
	}

	public static int lowerLimit(int[] a, int n) {
		int ans = 0;

		int ll = 0;
		int rl = a.length - 1;
		// System.out.println(a[rl]+" "+n);
		if (a[0] > n)
			return 0;
		if (a[0] == n)
			return 1;
		else if (a[rl] <= n)
			return rl + 1;

		while (ll <= rl) {

			int mid = (ll + rl) / 2;
			if (a[mid] == n) {
				ans = mid + 1;
				break;
			}

			else if (a[mid] > n) {
				rl = mid - 1;

			} else {
				ans = mid + 1;
				ll = mid + 1;
			}
		}

		return ans;
	}

	public static long choose(long total, long choose) {
		if (total < choose)
			return 0;
		if (choose == 0 || choose == total)
			return 1;
		return (choose(total - 1, choose - 1) + choose(total - 1, choose)) % mod;
	}

	public static int[] suffle(int[] a, Random gen) {
		int n = a.length;
		for (int i = 0; i < n; i++) {
			int ind = gen.nextInt(n - i) + i;
			int temp = a[ind];
			a[ind] = a[i];
			a[i] = temp;
		}
		return a;
	}

	public static int floorSearch(int arr[], int low, int high, int x) {
		if (low > high)
			return -1;

		if (x > arr[high])
			return high;
		int mid = (low + high) / 2;

		if (mid > 0 && arr[mid - 1] < x && x < arr[mid])
			return mid - 1;

		if (x < arr[mid])
			return floorSearch(arr, low, mid - 1, x);

		return floorSearch(arr, mid + 1, high, x);
	}

	public static void swap(int a, int b) {
		int temp = a;
		a = b;
		b = temp;
	}

	public static ArrayList<Integer> primeFactorization(int n) {
		ArrayList<Integer> a = new ArrayList<Integer>();
		for (int i = 2; i * i <= n; i++) {
			while (n % i == 0) {
				a.add(i);
				n /= i;
			}
		}
		if (n != 1)
			a.add(n);
		return a;
	}
	
	
	

	public static void sieve(boolean[] isPrime, int n) {
		for (int i = 1; i < n; i++)
			isPrime[i] = true;

		isPrime[0] = false;
		isPrime[1] = false;

		for (int i = 2; i * i < n; i++) {
			if (isPrime[i] == true) {
				for (int j = (2 * i); j < n; j += i)
					isPrime[j] = false;
			}
		}
	}

	public static int lowerbound(ArrayList<Long> net, long c2) {
		int i = Collections.binarySearch(net, c2);
		if (i < 0)
			i = -(i + 2);
		return i;

	}
	
	public static int lowerboundArray(int[] dis, int c2) {
		int i = Arrays.binarySearch(dis, c2);
		if (i < 0)
			i = -(i + 2);
		return i;

	}

	public static int uperbound(ArrayList<Integer> list, int c2) {
		int i = Collections.binarySearch(list, c2);
		if (i < 0)
			i = -(i + 1);
		return i;

	}

	public static int uperboundArray(int[] dis, int c2) {
		int i = Arrays.binarySearch(dis, c2);
		if (i < 0)
			i = -(i + 1);
		return i;

	}

	public static long[] sort(long[] a) {
		Random gen = new Random();
		int n = a.length;
		for (int i = 0; i < n; i++) {
			int ind = gen.nextInt(n - i) + i;
			long temp = a[ind];
			a[ind] = a[i];
			a[i] = temp;
		}

		Arrays.sort(a);
		return a;
	}

	public static int[] sort(int[] a) {
		Random gen = new Random();
		int n = a.length;
		for (int i = 0; i < n; i++) {
			int ind = gen.nextInt(n - i) + i;
			int temp = a[ind];
			a[ind] = a[i];
			a[i] = temp;
		}

		Arrays.sort(a);
		return a;
	}

	public static int GCD(int a, int b) {
		if (b == 0)
			return a;
		else
			return GCD(b, a % b);
	}

	public static long GCD(long a, long b) {
		if (b == 0)
			return a;
		else
			return GCD(b, a % b);
	}

	public static void extendedEuclid(int A, int B) {
		if (B == 0) {
			d = A;
			p = 1;
			q = 0;
		} else {
			extendedEuclid(B, A % B);
			int temp = p;
			p = q;
			q = temp - (A / B) * q;
		}
	}

	public static long LCM(long a, long b) {
		return (a * b) / GCD(a, b);
	}

	public static int LCM(int a, int b) {
		return (a * b) / GCD(a, b);
	}

	public static int binaryExponentiation(int x, int n) {
		int result = 1;
		while (n > 0) {
			if (n % 2 == 1)
				result = result * x;
			x = x * x;
			n = n / 2;
		}
		return result;
	}

	public static int[] countDer(int n) {
		int der[] = new int[n + 1];

		der[0] = 1;
		der[1] = 0;
		der[2] = 1;

		for (int i = 3; i <= n; ++i)
			der[i] = (i - 1) * (der[i - 1] + der[i - 2]);

		// Return result for n
		return der;
	}

	static long binomialCoeff(int n, int k) {
		long C[][] = new long[n + 1][k + 1];
		int i, j;

		// Calculate value of Binomial Coefficient in bottom up manner
		for (i = 0; i <= n; i++) {
			for (j = 0; j <= Math.min(i, k); j++) {
				// Base Cases
				if (j == 0 || j == i)
					C[i][j] = 1;

				// Calculate value using previosly stored values
				else
					C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
			}
		}

		return C[n][k];
	}

	public static long binaryExponentiation(long x, long n) {
		long result = 1;
		while (n > 0) {
			if (n % 2 == 1)
				result = result * x;
			x = (x % mod * x % mod) % mod;
			n = n / 2;
		}
		return result;
	}

	public static int modularExponentiation(int x, int n, int M) {
		int result = 1;
		while (n > 0) {
			if (n % 2 == 1)
				result = (result * x) % M;
			x = (x * x) % M;
			n = n / 2;
		}
		return result;
	}

	public static long modularExponentiation(long x, long n, long M) {
		long result = 1;
		while (n > 0) {
			if (n % 2 == 1)
				result = (result * x) % M;
			x = (x * x) % M;
			n = n / 2;
		}
		return result;
	}

	public static int modInverse(int A, int M) {
		return modularExponentiation(A, M - 2, M);
	}

	public static long sie(long A, long M) {
		return modularExponentiation(A, M - 2, M);
	}

	public static boolean checkYear(int year) {
		if (year % 400 == 0)
			return true;

		if (year % 100 == 0)
			return false;

		if (year % 4 == 0)
			return true;
		return false;
	}

	public static boolean isPrime(int n) {

		if (n <= 1)
			return false;
		if (n <= 3)
			return true;

		if (n % 2 == 0 || n % 3 == 0)
			return false;

		for (int i = 5; i * i <= n; i = i + 6) {
			if (n % i == 0 || n % (i + 2) == 0)
				return false;
		}

		return true;
	}

	static class pair implements Comparable<pair>

	{
		Long x, y;

		pair(long x, long y) {
			this.x = x;
			this.y = y;
		}

		public int compareTo(pair o) {
			int result = x.compareTo(o.x);
			if (result == 0)
				result = y.compareTo(o.y);

			return result;
		}

		public String toString() {
			return x + " " + y;
		}

		public boolean equals(Object o) {
			if (o instanceof pair) {
				pair p = (pair) o;
				if(p.x-x==0 && p.y-y==0)
					return true;
				else
				return false;
			}
			return false;
		}

		public int hashCode() {
			return new Long(x).hashCode() * 31 + new Long(y).hashCode();
		}

	}
	

	static class triplet implements Comparable<triplet> {
		Integer x, y, z;

		triplet(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}

		public int compareTo(triplet o) {
			int result = x.compareTo(o.x);
			if (result == 0)
				result = y.compareTo(o.y);
			if (result == 0)
				result = z.compareTo(o.z);

			return result;
		}

		public boolean equlas(Object o) {
			if (o instanceof triplet) {
				triplet p = (triplet) o;
				return x == p.x && y == p.y && z == p.z;
			}
			return false;
		}

		public String toString() {
			return x + " " + y + " " + z;
		}

		public int hashCode() {
			return new Long(x).hashCode() * 31 + new Long(y).hashCode() + new Long(z).hashCode();
		}
	}

	
	static class query implements Comparable<query> {
		Integer l,r, x, idx, tp;

	
		query(int l, int r, int x, int id, int tp)
		{
			this.l = l ;
			this.r = r;
			this.x = x;
			this.idx = id;
			this.tp = tp;
		}
		
		public int compareTo(query o) {
			int result = x.compareTo(o.x);
			
			return result;
		}

		
	

		
	}
	
	/*
	 * static class node implements Comparable<node>
	 * 
	 * { Integer x, y, z; node(int x,int y, int z) { this.x=x; this.y=y; this.z=z; }
	 * 
	 * public int compareTo(pair o) { int result = x.compareTo(o.x); if(result==0)
	 * result = y.compareTo(o.y); if(result==0) result = z.compareTo(z); return
	 * result; }
	 * 
	 * @Override public int compareTo(node o) { // TODO Auto-generated method stub
	 * return 0; } }
	 */
}